We define a local authority to be a hotspot if weekly cases per 100,000 population exceed 50. For past weeks we compare the observed cases to the threshold. For future weeks, we give probabilities based on our model, which assumes a situation in which no additional interventions (e.g. local lockdowns) occur. We consider a local authority to have increasing infections (likely increasing infections) if our model estimates that with probability of at least 90% (75%) the reproduction number Rt is greater than 1 . Decreasing and likely decreasing are defined analogously, but consider Rt less than 1 .
Median and 90% credible interval for weekly cases and Rt can be viewed via the “Column Visibility” button. Colour code for cases in table: ■ 0.00 – 0.25 ■ 0.25 – 0.50 ■ 0.50 – 0.70 ■ 0.70 – 0.90 ■ 0.90 – 0.95 ■ 0.95 – 1.00. Colour code for Rt in table: ■ 0.00 – 0.1 ■ 0.1 – 0.25 ■ 0.25 – 0.75 ■ 0.75 – 0.90 ■ 0.90 – 1.00.
The results on this page have been computed using epidemia 0.6.0. Epidemia extends the Bayesian semi-mechanistic model proposed in the Flaxman, S., Mishra, S., Gandy, A. et al. Nature 2020.
The model is based on a self-renewal equation which uses time-varying reproduction number \(R_{t}\) to calculate the infections. However, due to a lot of uncertainty around reported cases in early part of epidemics, we use observed deaths to back-calculate the infections as a latent variable. Then the model utilizes these latent infections together with probabilistic lags related to SARS-CoV-2 to calibrate against the observed deaths and the reported cases in the last 30 days. A detailed mathematical description of the model can be found here.
\(R_{t}\) for each local authority is parameterized as a linear function of the \(R_t\) for Engalnd and Wales as a whole (which we fit too), and a random effect specific to the local authority for each week over the course of the epidemic. The weekly random effects are encoded as a random walk, where at each successive step the random effect has an equal chance of moving upward or downward.
Authors: Swapnil Mishra1, Jamie Scott2, Harrison Zhu2, Neil Ferguson1, Samir Bhatt1, Seth Flaxman2, Axel Gandy2
1MRC Centre for Global Infectious Disease Analysis, Jameel Institute for Disease and Emergency Analytics, Imperial College London
2Department of Mathematics, Imperial College London
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Corresponding Author
Axel Gandy
a.gandy@imperial.ac.uk
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